Thanks for the reply. I had tried replacing the OR with an AND, and I still get the same results.
IF EXISTS(SELECT F00069, F00026, F01298, F01299, F01300
FROM patient INNER JOIN
tumor ON patient.UK = tumor.FK1 INNER JOIN
followup ON tumor.FK1 = followup.FK1 INNER JOIN
hospital ON tumor.UK = hospital.FK2
WHERE (hospital.F00026 = '0' OR hospital.F00026 = '1' OR hospital.F00026 = '2')
AND patient.F00069 = '1' AND followup.F01298 = ' ' AND followup.F01299 = ' ' AND followup.F01300 = ' ')
UPDATE followup SET followup.F01298 = 'C', followup.F01299 = 'C', followup.F01300 = 'C'
PRINT 'Nothing to Update'